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Laminar natural convection from a horizontal plate and the influence of plate-edge extensions

Published online by Cambridge University Press:  20 April 2006

R. J. Goldstein  and
Kei-Shun Lau
R. J. Goldstein
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
Kei-Shun Lau
Affiliation:
Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
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Abstract

Laminar natural convection from a horizontal plate is studied by a finite-difference analysis and by experiments for Rayleigh numbers from 10 to 104. The plate with uniform surface temperature or concentration on one side and insulated on the other is situated in an ‘infinite’ fluid medium. The buoyancy near the surface is directed either outward or inward normal to the active surface – equivalent to a heated plate facing upward or downward. The effect of insulated vertical and horizontal extensions to the plate are also examined.

Finite-difference solutions are obtained for a heated strip in a two-dimensional domain for a Prandtl number of 0·7. Mass-transfer experiments are performed with square naphthalene plates in air. Both numerical and experimental results justify a 1/5-power law in the present range of Rayleigh number – i.e. Nusselt number or Sherwood number proportional to the Rayleigh number raised to the 1/5 power. The horizontal extensions cause a limited reduction in the transfer rate for the plate generating ‘outward buoyancy’, and a larger reduction with ‘inward buoyancy’. The vertical walls block the fluid flow directly, and thus greatly lower the transfer rate with either outward or inward buoyancy.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 129 , April 1983 , pp. 55 - 75
Copyright
© 1983 Cambridge University Press

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